POLARON STATES AND WEAK SELF-TRAPPING IN 2 DIMENSIONS

States of polarons interacting with phonons via short-range forces in two dimensions depend strongly on whether phonons give rise to changes in potentials or transfer integrals for polarons. At a nonvanishing critical coupling, polarons become associated suddenly with a strong local lattice distortion in the former, dropping into a small-radius self-trapped state (STS), while with an infinitesimal but infinitely extended one in the latter, dropping into a large-radius weak STS. Below the critical coupling, polarons can move freely, but do so in a new state of binding with phonons where the phonon energy quantum is greatly reduced around them from its original value.